Properties

Label 157200.a
Number of curves $2$
Conductor $157200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 157200.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157200.a1 157200bp1 \([0, -1, 0, -28408, 1843312]\) \(39616946929/226368\) \(14487552000000\) \([2]\) \(552960\) \(1.3668\) \(\Gamma_0(N)\)-optimal
157200.a2 157200bp2 \([0, -1, 0, -12408, 3891312]\) \(-3301293169/100082952\) \(-6405308928000000\) \([2]\) \(1105920\) \(1.7134\)  

Rank

sage: E.rank()
 

The elliptic curves in class 157200.a have rank \(1\).

Complex multiplication

The elliptic curves in class 157200.a do not have complex multiplication.

Modular form 157200.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.